Speaking at the Center for Strategic and International Studies Wednesday morning, Mr. Shanahan said he hasn’t “walked through the proposal” with committee Chairman Adam Smith, Washington state Democrat, but explained “there’s been less pushback” on a proposal that is a top military priority of President Trump.

Mr. Smith in the past has opposed the idea of a Space Force as a sixth branch of the military, and has cited the cost as a key reason the initiative shouldn’t go forward.

The Trump administration now wants to phase in a Space Force over five years beginning with the fiscal 2020 budget year. That would add an estimated $2 billion in costs beyond what is spent on existing military space activities.

Mr. Shanahan, who is believed to be auditioning for a permanent appointment to the Pentagon’s top post, spoke just hours before the Defense Department’s inspector general announced plans to open an investigation into the former Boeing executive’s relations with his onetime employer since coming to the Pentagon in 2017.

Citizens for Responsibility and Ethics, a Washington-based watchdog group, filed an ethics complaint asking the inspector general to investigate reports that Mr. Shanahan touted Boeing’s line of aircraft over rival Lockheed Martin.

Shanahan spokesman Army Col. Joseph Buccino said Mr. Shanahan welcomed the review, saying the acting secretary is “committed” to observing his ethics agreement.

“This agreement ensures any matters pertaining to Boeing are handle by appropriate officials within the Pentagon to eliminate any perceived or actual conflict of interest issue with Boeing,” Col. Buccino said.

On the Space Force, the acting secretary defended the $2 billion price tag Wednesday, calling it a “top-down number,” but added, “I think we’ll get the cost piece right.”

Mr. Shanahan said lawmakers have expressed concern about the Space Force plan creating bureaucracy. “I don’t blame them,” he said, and explained “we have to be very thoughtful about managing bureaucracy.”

Speaking ahead of Mr. Shanahan, Rep. Jim Cooper, chairman of the committee’s subcommittee on space, expressed optimism of the proposal’s progress on Capitol Hill. “The prospects could hardly be brighter,” he said.

The Tennessee Democrat said Mr. Trump’s original idea for the Space Force was “over the top,” but that the current proposal is “way more modest,” and “about as close to our original House proposal as you can get.”

“My guess is from the administration’s standpoint, they mainly care that we call it a ‘Space Force,’ whatever we’re doing,” Mr. Cooper added.

During his discussion at CSIS, Mr. Shanahan revealed that plans now call for a Space Force of about 15,000 and 20,000 people, which he noted “won’t be very large,” and its budget, which he said will be similar to the U.S. Special Operations Command.

The acting defense secretary is set to testify before the committee Tuesday on the 2020 defense budget, and will likely face questions from lawmakers of both parties on the Space Force proposal and its cost.